{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaptive Kalman Filter Implementation for Constant Velocity Model (CV) in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Image](http://www.cbcity.de/wp-content/uploads/2013/06/Fahrzeug_GPS_Tunnel-520x181.jpg)\n",
    "\n",
    "Situation covered: You drive with your car in a tunnel and the GPS signal is lost. Now the car has to determine, where it is in the tunnel. The only information it has, is the velocity in driving direction. The x and y component of the velocity ($\\dot x$ and $\\dot y$) can be calculated from the absolute velocity (revolutions of the wheels) and the heading of the vehicle (yaw rate sensor)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constant Velocity Model for Ego Motion\n",
    "\n",
    "$$x= \\left[ \\matrix{ x \\\\ y \\\\ \\dot x \\\\ \\dot y} \\right]$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Formal Definition:\n",
    "\n",
    "$$x_{k+1} = \\textbf{A} \\cdot x_{k}$$\n",
    "\n",
    "$$x_{k+1} = \\begin{bmatrix}1 & 0 & \\Delta t & 0 \\\\ 0 & 1 & 0 & \\Delta t \\\\ 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\end{bmatrix}_{k}$$\n",
    "\n",
    "$$y = \\textbf{H} \\cdot x$$\n",
    "\n",
    "$$y = \\begin{bmatrix}0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 1\\end{bmatrix} \\cdot x$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.]]), (4, 1))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x106da6190>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/paul/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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AnJ1kQ5LjgUu7dtMt2oAkSYuvT1i8H3h5kvuBC7t5kpyR5DMAVfU0cAVwK/BV4KNVtaur\ne22SfcAm4DNJPtujL5KkMVrwZail4mUoSZq/lXQZSpJ0lDAsJElNhoUkqcmwkCQ1GRaSpCbDQpLU\nZFhIkpoMC0lSk2EhSWoyLCRJTYaFJKnJsJAkNRkWkqQmw0KS1GRYSJKaDAtJUpNhIUlqMiwkSU2G\nhSSpybCQJDUZFpKkJsNCktRkWEiSmgwLSVKTYSFJajIsJElNhoUkqcmwkCQ1LTgskpyS5PYk9ye5\nLcnaGeo2J9md5IEkVw4t/80ku5Lck+QTSU5eaF8kSePV58ziHcDtVXUO8Llu/jBJ1gDXAZuB84Ct\nSc7tVt8GvLCqXgTcD1zVoy+SpDHqExYXA9u66W3Aa0bUbAT2VNXeqnoKuBm4BKCqbq+qZ7u6O4F1\nPfoiSRqjPmFxalUd6KYPAKeOqDkT2Dc0/2C3bLpfAHb06IskaYyOnW1lktuB00aseufwTFVVkhpR\nN2rZ9H28E3iyqv6oVStJWh6zhkVVvXymdUkOJDmtqh5OcjrwzRFl+4H1Q/PrGZxdHNzGG4EtwMtm\n68fk5OSh6YmJCSYmJmYrl6SjztTUFFNTU2PbfqqaH/5HN0yuAb5dVVcneQewtqreMa3mWOBrDMLg\nIeAuYGtV7UqyGfht4KVV9a1Z9lML7aMkHa2SUFVZtO31CItTgI8BZwF7gddV1aNJzgD+oKpe2dVd\nBFwLrAFuqKr3dcsfAI4HHuk2+adV9dYR+zEsJGmeVkxYLBXDQpLmb7HDwje4JUlNhoUkqcmwkCQ1\nGRaSpCbDQpLUZFhIkpoMC0lSk2EhSWoyLCRJTYaFJKnJsJAkNRkWkqQmw0KS1GRYSJKaDAtJUpNh\nIUlqMiwkSU2GhSSpybCQJDUZFpKkJsNCktRkWEiSmgwLSVKTYSFJajIsJElNhoUkqcmwkCQ1GRaS\npKYFh0WSU5LcnuT+JLclWTtD3eYku5M8kOTKoeXvSXJPki8luTXJ6QvtiyRpvPqcWbwDuL2qzgE+\n180fJska4DpgM3AesDXJud3qa6rqRVV1PvBp4Nd79OWINTU1tdxdGKvVPL7VPDZwfDpcn7C4GNjW\nTW8DXjOiZiOwp6r2VtVTwM3AJQBV9ddDdScBz/boyxFrtf+FXc3jW81jA8enwx3bo+2pVXWgmz4A\nnDqi5kxg39D8g8BLDs4k+Q3gMuAxYKJHXyRJYzTrmUV3T+LeET8XD9dVVQE1YhOjlg23e2dVnQX8\nF+CX5tt5SdLSyOD3/AIaJruBiap6uLs5vbOqXjCtZhMwWVWbu/mrgGer6uppdWcBn6mqnxixn4V1\nUJKOclWVxdpWn8tQ24E3AFd3//3kiJovAGcn2QA8BFwKbAVIcnZVPdDVXQLsGrWTxRysJGlh+pxZ\nnAJ8DDgL2Au8rqoeTXIG8AdV9cqu7iLgWmANcENVva9b/nHg7zC4sb0X+MWq+oteo5EkjcWCw0KS\ndPRYlje4F+GFvp9Lcl+SZ5K8eGj5hiRPdC/6fSnJf1yK8Yzo91jG1627qqvfneQfj3ssoyzC+Ea2\nX+7jN1N/p9V8oFt/T5LzW23n+me1FMY0vskkDw4ds81LMZYR/e4ztj9MciDJvdPqV8uxm2l88zt2\nVbXkP8A1wL/tpq8E3j+iZg2wB9gAHAd8GTi3W/cC4BxgJ/DioTYbgHuXY0xLNL7zurrjunZ7gGOO\nwPGNbL+cx2+2/g7VbAF2dNMvAf73Qse6isb3LuBtyzGmxRhbN/+PgPOn/91bDceuMb55Hbvl+m6o\nvi/07a6q+5ekpwszrvFdAnykqp6qqr0M/gJtXOzOz0Gv8c2x/VKbrb8HHep3Vd0JrE1yWqPtShnr\nuMYHsNwPofQZG1X1eeA7I7a7Go7dbOODeRy75QqLhb7Qd+Yctv1j3SnVVJKf6dnPhRrX+M7o6ubT\nZhz6jm+29st1/OZyPGaqOWOWtnP5s1oK4xofwC91lz5uWKZLNX3GNpvVcOxa5nzs+jw6O6sktwOn\njVj1zuGZqqqMfpdiIXfeHwLWV9V3umv9n0zywjr8q0UWxTKNb5SxPKEwhvFlxLLp7Zfs+I0w1z/H\nuXwSm8tYl9pijm/Y9cC/76bfA/w28OZ5bqOvhY5tzsfiCD12rXbzOnZjC4uqevlM67qbLafVD1/o\n++aIsv3A+qH59Rz+qXrUPp8Enuymv5jkz4GzgS/Ot/8tyzG+EW3WdcsW3RjGN9zXke2X8vjNob+j\njseoMT3I4DryvMa6DBZzfIfaVtWh8ST5EPCpxevynC10bK1/O0f6sZt1fPM9dst1GergC30whxf6\nkhzP4IW+7SPqDqVpkudl8E23JPnbDH7RfH0xOz5HYxlft/6fJzk+yY8xGN9di9ftOes7vpHtl/n4\nzeV4bAde3/VvE/Bod5li3mNdBmMZXw7/Xwu8FriXpddnbLNZDcduRvM+dst0d/8U4L8B9wO3AWu7\n5Wcw+NqPg3UXAV9jcCP3qqHlr2Vwfe4J4GHgs93yfwp8BfgS8H+AV66m8XXr/l1Xvxt4xRE6vpna\n/5PlPH6j+gtcDlw+VHNdt/4eDn9SbV5jXabjNo7x3Qj8WVf/SQbX+Y+0sX2EwSXQH3T/7t60yo7d\nTOOb17HzpTxJUpP/W1VJUpNhIUlqMiwkSU2GhSSpybCQJDUZFpKkJsNCktRkWEiSmv4/p4dPzSiC\nXkMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c22c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.matrix([[0.0, 0.0, 0.0, 0.0]]).T\n",
    "print(x, x.shape)\n",
    "plt.scatter(float(x[0]),float(x[1]), s=100)\n",
    "plt.title('Initial Location')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.]]), (4, 4))\n"
     ]
    },
    {
     "data": {
      "image/png": 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RMmH3Jn+K/Up6LXBZRPTm0/8EDEbEZwttvgT0RcTSfHotcEZEPNys/1EZAbd7\nc8zMRlKJ+bMKmCFpOjAAXADMa2hzI7AAWJoH9h9bhS94E4SZWUciYqekBcByoAdYEhFrJM3Ply+O\niB9KOlfSeuBPwEXt+hyVTRBmZvZ8PgrCzCwRB7BZA0kvkLQiP+PpsNT1WH05gM2ebx+y4zlfChyQ\nuJbK8D+m8nknnFmDiHhG0jHAxIh4KnU9FTL0j+lAsn9Mj6ctZ+zzTrhxSNKhwJXAvsBEYF5E7Cos\nXwQcGhHvSFSiVZSk/fE/ptI4gMehPGA/AzwBbAXOi4ib82UTgT8CyyLi/HRVpiHpRcClZGczzQC+\nAtwKXAFsBw4BFkbEQ8mKtNqo/SYI/0E9l6RjgS0RsUnSefnsLYUmpwD7Az8e9eISk7QvsARYkL8/\nM4GVwE3AfGAu2e/Pr4DPJyt0lPkT08ipdQD7D6qpycB1+ffvAzZExIrC8tPzr7eNalXVMB+4KiI2\n5dPbyAJndUQ8lp/Seg/Z78948kngEv78iekGoPiJ6SJgWbLqxrC6HwXR9g+K7CIZ4+oPKiLuiIgH\n80vkncufw3jI64GHI2LN6FeX3OMRUfzHc3L+9RaAiLg2Ik6KiHWjX1oaxU9MwFn5bH9iKkndA9h/\nUK2dT3Y65beHZkiaAJwG9CWqKamI+EbDrDOBJ4G7E5RTFf7ENIJqvQnCf1BtnQoMNPzzORE4GP8x\nDTkL+FmM4z3VEXEHQOET02UNTcbzJ6a9VvcRcKNx/wdV8GLg9w3zzsm/jvsAlnQkcAxwe8P8thdX\nqTF/YhoB4yaA/Qf1PCuB6fkfEfnNAy8BNo/HTTKSJudneV2ez+rNv64qtDkWeMWoF1cN/sQ0Amq7\nCULSZLI9tf8nIj6O/6AafQo4CrhZ0u+Ap8lGOD9KWlU6Z5DtUPqBpBcCbybb2TQJdh/OeDnZdtDx\nyJ+YRkBtAxj/QQ0rIt499L2k88lOL/1auoqSWkZ2yOIUsjvffgiYBlwiaS7Zp8WLx/EZYCuB90ia\nEBGD4/0TU1lqeyZcHrpfAJ4lC5ZPkP9Bkd00bwLZ7UX6U9WYiqTlwOuAIyJia74Z4i6yP6a3pq3O\nqig/BflLZCPhoU9MC4DvRMSFCUsb02obwNaapMfINsX0kv0jugqYCbwpIv6UsjarJkn7R8S2wvT5\nZDvkzokIHwO8hxzA45Ckc4A3kh1APwW4E7g6IgaTFmaV5E9MI8cBbGZt+RPTyHEAm1lb/sQ0chzA\nZmaJjJujfsjaAAAANUlEQVQTMczMqsYBbGaWiAPYzCwRB7CZWSIOYDOzRBzAZmaJOIDNzBJxAJuZ\nJeIANjNL5P8D+6leJSvwLQkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c29850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = 1.0*np.eye(4)\n",
    "print(P, P.shape)\n",
    "\n",
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Initial Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dynamic Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is calculated from the dynamics of the Egomotion.\n",
    "\n",
    "$$x_{k+1} = x_{k} + \\dot x_{k} \\cdot \\Delta t$$\n",
    "$$y_{k+1} = y_{k} + \\dot y_{k} \\cdot \\Delta t$$\n",
    "$$\\dot x_{k+1} = \\dot x_{k}$$\n",
    "$$\\dot y_{k+1} = \\dot y_{k}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 1. ,  0. ,  0.1,  0. ],\n",
      "        [ 0. ,  1. ,  0. ,  0.1],\n",
      "        [ 0. ,  0. ,  1. ,  0. ],\n",
      "        [ 0. ,  0. ,  0. ,  1. ]]), (4, 4))\n"
     ]
    }
   ],
   "source": [
    "dt = 0.1 # Time Step between Filter Steps\n",
    "\n",
    "A = np.matrix([[1.0, 0.0, dt, 0.0],\n",
    "              [0.0, 1.0, 0.0, dt],\n",
    "              [0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 1.0]])\n",
    "print(A, A.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We directly measure the Velocity $\\dot x$ and $\\dot y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.,  0.,  1.,  0.],\n",
      "        [ 0.,  0.,  0.,  1.]]), (2, 4))\n"
     ]
    }
   ],
   "source": [
    "H = np.matrix([[0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 1.0]])\n",
    "print(H, H.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement Noise Covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R will be updated in each filter step in the adaptive Kalman Filter, here is just the initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 1.,  0.],\n",
      "        [ 0.,  1.]]), (2, 2))\n"
     ]
    },
    {
     "data": {
      "image/png": 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Z2TwzW2Vmq83stmHW+WJ5+eNmdnHF++vM7AkzW2FmjybZ8Fb0/PP5h2rSJOjq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c22a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ra = 1.0**2\n",
    "\n",
    "R = np.matrix([[ra, 0.0],\n",
    "              [0.0, ra]])\n",
    "print(R, R.shape)\n",
    "\n",
    "\n",
    "# Plot between -10 and 10 with .001 steps.\n",
    "xpdf = np.arange(-10, 10, 0.001)\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(xpdf, norm.pdf(xpdf,0,R[0,0]))\n",
    "plt.title('$\\dot x$')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(xpdf, norm.pdf(xpdf,0,R[1,1]))\n",
    "plt.title('$\\dot y$')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Process Noise Covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Position of the car can be influenced by a force (e.g. wind), which leads to an acceleration disturbance (noise). This process noise has to be modeled with the process noise covariance matrix Q.\n",
    "\n",
    "$$Q = \\begin{bmatrix}\\sigma_{x}^2 & \\sigma_{xy} & \\sigma_{x \\dot x} & \\sigma_{x \\dot y} \\\\ \\sigma_{yx} & \\sigma_{y}^2 & \\sigma_{y \\dot x} & \\sigma_{y \\dot y} \\\\ \\sigma_{\\dot x x} & \\sigma_{\\dot x y} & \\sigma_{\\dot x}^2 & \\sigma_{\\dot x \\dot y} \\\\ \\sigma_{\\dot y x} & \\sigma_{\\dot y y} & \\sigma_{\\dot y \\dot x} & \\sigma_{\\dot y}^2 \\end{bmatrix}$$\n",
    "\n",
    "One can calculate Q as\n",
    "\n",
    "$$Q = G\\cdot G^T \\cdot \\sigma_v^2$$\n",
    "\n",
    "with $G = \\begin{bmatrix}0.5dt^2 & 0.5dt^2 & dt & dt\\end{bmatrix}^T$ and $\\sigma_v$ as the acceleration process noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sv = 1.0\n",
    "\n",
    "G = np.matrix([[0.5*dt**2],\n",
    "               [0.5*dt**2],\n",
    "               [dt],\n",
    "               [dt]])\n",
    "\n",
    "Q = G*G.T*sv**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0.25 dt^{4} & 0.25 dt^{4} & 0.5 dt^{3} & 0.5 dt^{3}\\\\0.25 dt^{4} & 0.25 dt^{4} & 0.5 dt^{3} & 0.5 dt^{3}\\\\0.5 dt^{3} & 0.5 dt^{3} & dt^{2} & dt^{2}\\\\0.5 dt^{3} & 0.5 dt^{3} & dt^{2} & dt^{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡       4         4        3        3⎤\n",
       "⎢0.25⋅dt   0.25⋅dt   0.5⋅dt   0.5⋅dt ⎥\n",
       "⎢                                    ⎥\n",
       "⎢       4         4        3        3⎥\n",
       "⎢0.25⋅dt   0.25⋅dt   0.5⋅dt   0.5⋅dt ⎥\n",
       "⎢                                    ⎥\n",
       "⎢      3         3       2        2  ⎥\n",
       "⎢0.5⋅dt    0.5⋅dt      dt       dt   ⎥\n",
       "⎢                                    ⎥\n",
       "⎢      3         3       2        2  ⎥\n",
       "⎣0.5⋅dt    0.5⋅dt      dt       dt   ⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, Matrix\n",
    "from sympy.interactive import printing\n",
    "printing.init_printing()\n",
    "dts = Symbol('dt')\n",
    "Qs = Matrix([[0.5*dts**2],[0.5*dts**2],[dts],[dts]])\n",
    "Qs*Qs.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IeILk6Ina+9EXX2wsfy29VeGvpbdKRb+WfvLkyQ1t97bbbmurr6U3MytNu5wJ5wA2s5bj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\nyf8HoGmGvHYe3XoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1085a70d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Identity Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.]]), (4, 4))\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(4)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 200)\n"
     ]
    }
   ],
   "source": [
    "m = 200 # Measurements\n",
    "vx= 20 # in X\n",
    "vy= 10 # in Y\n",
    "\n",
    "mx = np.array(vx+np.random.randn(m))\n",
    "my = np.array(vy+np.random.randn(m))\n",
    "\n",
    "# some different error somewhere in the measurements\n",
    "my[(m/2):(3*m/4)]= np.array(vy+20.0*np.random.randn(m/4))\n",
    "\n",
    "measurements = np.vstack((mx,my))\n",
    "\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x108753450>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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V7nfqF2tRB4Kqb7f9pIkvr+Sk6vrt12kumqAe8ipsVKn2BUB5qpZkFBVPHcs2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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1085c6f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,5))\n",
    "\n",
    "plt.step(range(m),mx, label='$\\dot x$')\n",
    "plt.step(range(m),my, label='$\\dot y$')\n",
    "plt.ylabel('Velocity')\n",
    "plt.title('Measurements')\n",
    "plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "xt = []\n",
    "yt = []\n",
    "dxt= []\n",
    "dyt= []\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Rdx= []\n",
    "Rdy= []\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Kalman Filter](https://raw.github.com/balzer82/Kalman/master/Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for n in range(len(measurements[0])):\n",
    "    \n",
    "    # Adaptive Measurement Covariance R from last i Measurements\n",
    "    # as an Maximum Likelihood Estimation\n",
    "    i = 10\n",
    "    if n>i:\n",
    "        R = np.matrix([[np.std(measurements[0,(n-i):n])**2, 0.0],\n",
    "                      [0.0, np.std(measurements[1,(n-i):n])**2]])\n",
    "    \n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    x = A*x\n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = A*P*A.T + Q\n",
    "    \n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # Compute the Kalman Gain\n",
    "    S = H*P*H.T + R\n",
    "    K = (P*H.T) * np.linalg.pinv(S)\n",
    "\n",
    "    \n",
    "    # Update the estimate via z\n",
    "    Z = measurements[:,n].reshape(2,1)\n",
    "    y = Z - (H*x)                            # Innovation or Residual\n",
    "    x = x + (K*y)\n",
    "    \n",
    "    # Update the error covariance\n",
    "    P = (I - (K*H))*P\n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "    # Save states for Plotting\n",
    "    xt.append(float(x[0]))\n",
    "    yt.append(float(x[1]))\n",
    "    dxt.append(float(x[2]))\n",
    "    dyt.append(float(x[3]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))\n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Rdx.append(float(R[0,0]))\n",
    "    Rdy.append(float(R[1,1]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thats it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's take a look at the filter performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Gains K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109327ed0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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ezhk6dCj279+POXPmoKamBlu2bEF+fj4SEhLw1ltvYf369V7H6c5DDz2E3/zm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\nBQAAAAD4NRJXAAAAAIBf+z8kmVcSKcwVtQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10775e690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
    "plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nP39e02YK8KGOF1cO/sQ0BCo7BSFpX7IztT+KiEvwG6re5cDBwL2Sfg28TjbC\n+XHSqtKZRnZC6V8l7Q58guxk0x6w43LGeWTzoCORPzENgcoGMH5DDSoiPtf/XNJMsttLb0lXUVIL\nyC5ZHA9cC1xI9ufFL5V0NtmnxYtG8B1gjwF/LmlURGwf6Z+Y2qWyd8LloXsVsI0sWOaSv6GAtWRv\nqDkRsTpVjalIegA4ATgwIjbn0xA/I3sz/Una6qyM8luQ/4lsJNz/iWk2cFdEnJewtGGtsgFsjUl6\nmWwq5nSyX0RXA0cAZ0TEGylrs3KSNCYiemuWZ5KdkDs1InwN8E5yAI9Akk4FTiO7gH488FPgmojY\nnrQwKyV/Yho6DmAza8qfmIaOA9jMmvInpqHjADYzS2TE3IhhZlY2DmAzs0QcwGZmiTiAzcwScQCb\nmSXiADYzS8QBbGaWiAPYzCwRB7CZWSL/H7g5GurNENiUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10968cc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1098b26d0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YWwMDA/rc5z6nYDCoqakpvfDCC/L5fDPPP/XUUxoYGNC3vvUtF6sEAAAAgKXhljebzFNP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\nhFYAAABWS2gFAABgtf4fWuRQ5vOpRIMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108778b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.semilogy(range(len(measurements[0])),Px, label='$x$')\n",
    "plt.semilogy(range(len(measurements[0])),Py, label='$y$')\n",
    "plt.semilogy(range(len(measurements[0])),Pdx, label='$\\dot x$')\n",
    "plt.semilogy(range(len(measurements[0])),Pdy, label='$\\dot y$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### State Estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x106f37510>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sIgAAANiBXoLsoa21CzMVZtNa+8lgSwIAAID59RJkH66qvbdeqapDkzw8uJIA\nAABgfrvNd0dV/V9J/jzJmiRfSHJQVf15khcl+a1hFAcAAACz7ej0O29N8qtJnpHki0nuSvKNJNe1\n1n4w0KLMWgwAADCxBn76nao6OMmvTV/2ylQr7SWttdv7XemCRQmyAAAAE2uo55Gtqhdkahbj57bW\nntjvSntYjyALAAAwoYZxHtndquoV0+NjL0vyrST/st8VAgAAwK7Y0RjZl2aqO/EpSb6e5JIkf9la\n+8eBF6VFFgAAYGINrGtxVX05U+H1L1prG/pdQV9FCbIAAAATa6hjZIdFkAUAAJhcAx8jCwAAAONk\noEG2qj5WVeur6tYZt32gqr5ZVTdX1X+pqicPsgYAAAAmy6BbZC9OcvKs276Y5MjW2vOS3J7kXQOu\nAQAAgAky0CDbWvtKko2zbru8tbZl+ur1SQ4aZA0AAABMllGPkT09yedHXAMAAAAdMrIgW1W/neSR\n1tqfj6oGAAAAume3Uay0qn4rycuTvGS+x6xZs2bb/1evXp3Vq1cPuiwAAAAGYN26dVm3bt2iLW/g\n55GtqoOTrG2tPXf6+slJfj/Jca21H8zzN84jCwAAMKF29TyyAw2yVXVJkuOSPDXJ+iTvydQsxcuS\nbJh+2Ndaa2+e9XeCLAAAwIQa6yDbL0EWAABgcu1qkB31rMUAAACwUwRZAAAAOkWQBQAAoFMEWQAA\nADpFkAUAAKBTBFkAAAA6RZAFAACgUwRZAAAAOkWQBQAAoFMEWQAAADpFkAUAAKBTBFkAAAA6RZAF\nAACgUwRZAAAAOkWQBQAAoFMEWQAAADpFkAUAAKBTBFkAAAA6RZAFAACgUwRZAAAAOkWQBQAAoFME\nWQAAADpFkAUAAKBTBFkAAAA6RZAFAACgUwRZAAAAOkWQBQAAoFMEWQAAADpFkAUAAKBTBFkAAAA6\nRZAFAACgUwRZAAAAOkWQBQAAoFMEWQAAADplt1EXAAAA42TFhSuy8aGN264v33N5NrxjwwgrAmYT\nZAEAYIaND21Me0/bdr3OrxFWA8xFkAUAYEGzWykTLZXA6AiyAAAsaHYrZTIZLZXzBXRgvAmyMGLG\n4QDA6MwV0IHxJ8jCiBmHAwCDoTs0TC5BFoaol+5Ly/dc/rgw60cXgEGb6zdqpi50t52rl9Ps1tYV\nF67Y7ne2C9sFi2WSegIKsjBEvXRfmuvLZK4f3a5+6QAwfL3svE5CF9t+f2dhqZiknoCCLHTA7B/d\nLn/pADAtTt/mAAAgAElEQVR8k7TzCoy/+Xp4LObBMkGWzjDOBQAWtivDWLrEbMMwvobRw0OQpTMm\nddr/fhhHC7A4+hkvNu5jzLrYvbaX57SX8a/D4uA6XdDPQa0uvY8FWcbWXD9YTJnrC2aYoX7cd+KW\nKjtWsPNmh77ZcxIkj/8cjbKb7iR8zufbhoWe03Eaw+vgOuOon4M9izV8bRT77YIsY2ucfrD6Nalh\nvJ8dPwbPjhWTapjhrdcJ93bWYm3DXJ/zrs3C28Xf97larRZ6zHzL8dvIYujlgNAwjeJzPdAgW1Uf\nS3JKku+31p47fduKJJ9M8uwkdyZ5VWvt/kHWwfjrd5zLuHeH6OKPdT9G3ULMrtHCzrgb9UGaxfg8\nDHIbJvHzOm5jeHt5jnt5jN/G7hj338Zh7mOO63Mx6BbZi5P8xyR/OuO2dya5vLX2/qp6x/T1dw64\nDsZcvx/GYc7mu9D59eYyyh/dSeh+xk/18v7r9/2mhZ1x00tvlnE/kNmPQX7Ou6brr+V8tNqOxmKM\nwV4qv43zHUQax1nPBxpkW2tfqaqDZ938iiTHTf//40nWRZCdeJNwkvWuta4u1tF/s0IOXi8HHRbr\n/dfL6+lcxoxaP5MVjdtOZr9hvEu/M0lvBxQmdZhNPwbVauvg9Y71Mq59oe+dYfY+G+VBrS69Z0Yx\nRvaA1tr66f+vT3LACGqYKF348upaCOyifsbv9PI+GeVr14X39mIY5pi3LvR+YGlZrINl4zbEoYsz\nB/ejl+8G+wCLr5dJfYb1/u/lt3rcfs/Hrev6bOP+mRmX569aG+yTNN0iu3bGGNmNrbXlM+7f0Fpb\nMetv2qmnnrrt+nOe85wcfvjhA60TAACAwfj2t7+d22+/fdv1z372s2mt9X3EZRQtsuur6mdba/9Q\nVU9P8v25HrR27dohl9VddX7NeRRunI7kDKuexVrPuD1/wzSoAf39LLcL7+3FMMhtGtYEDYu1DeN2\n1H6xzH5+xu193MvzPqhtGOZzManvLyZbv7+Fi/HZ6mXdcz2ml9+eQX32h/md0stz0U894/YbMShV\nu9ZrYBRB9i+TvCbJhdP/fmYENXSasSY7p98B/kvVoHboBtU1ddQ7pgu9v0Zd37DWM183o0GdWkTw\nWFyD6t4+bpMXed/AcAzqszbq39TZehnWxeAM+vQ7l2RqYqenVtVdSX43yfuSfKqqXpfp0+8MsoZJ\nNO795kepl5nW5psQxHM6XKMOPovVUrnQBBKTcM7HXvQ7PrGXg0j9HAQZ5M5O12Yw79dCz1Uvn2G/\nV7DrFms84mJ9L44yvI36VFyzOTg2WoOetfjX57nrxEGul8k8LUEvFus8bwxerzPjztbLD2g/k4/s\nSjja1fomVa+nmRhE0Bnkzo5wNmXcJleCSbVYvxm9fC/2c3BxsfTbg2PcW0WX6j75MIyia/GSNcyT\nCfeyIz+ssZBblw0LGfcDEUtlFtLFMqjnoteADLCU9RPwhnmgbrFOPzXuv7v97pOzMEF2iPppARqk\nQdWjtYIuWqyuzgxev6+Jo+LAUtLL99soWzN9//6Ufef+CLIDtNDRlWHuOI/L+Z5gFHp5/+smOfnm\nGie90HewHiY7Z9y7+AHbEybpMkF2gBY6utLrGMHF+JIZ5BeV7hCMu8VswWNy9HLwwlHynWOnGIBh\nEWTHzKBOUbJY5mudsKPHJLJTDgAsJr0kF48gy07ROgEAAP1xkHzxCLKLZFDjqEZ91Ea3YWAp0Z0c\nALpBkF0kg2qpHPVRGy2wwFIy6u/cYXGQEoCuE2T7NIk7AaNu/QVgOBykBKDrBNkeLJUJjpZKSwTA\nUuIUQsA4qRqviUxZfK0NJyMJsj1w5BqArpirx5DfMGCcDCvoMHzDPFAhyM5hErsNA7A0OPgKwFIg\nyM7BTgAA42iuA62GhQCwFAmyANARsw+0rrhwhUn6AFiSBFkAGLL5Zomf2brayyRNWmMBWKoEWQAY\nsrkC6Oxga5gLAMxPkAWAMTC7lVYXYQCY35IPss6vB8A40E0YAHq35IOsrlsAAADd8oRRFwAAAAA7\nQ5AFAAAYM4888kiOOuqoHHHEEdmwwfCT2QRZAACAMfPoo4/mnnvuyb333ptNmzaNupyxs+THyAIA\nAIybvffeO3fccUc2b96cfffdd9TljB1BFgAAYAzttdde2WuvvUZdxlhackF29ul2nGoHAAAYJz/8\n4Q9z/vnnp7WW73znOznjjDNy4okn5txzz80ee+yR+++/PxdeeGGe/vSnj7rUkVlyQdbpdgAAgHH1\n8MMP53Wve10+/OEP56CDDsott9ySVatW5bTTTstHPvKRfOYzn8kZZ5yR5z//+TnnnHNGXe7ILLkg\nCwAAdFPV6NbdhtQW9pGPfCRnn312DjrooCRT3Ys3b96cF7zgBdlvv/1SVXne856X0047bTgFjamJ\nCrJzdRve8A5TVQMAwCQYVpgcpRUrVuT444/fdv0b3/hGkuTkk09Okpx++uk5/fTTR1LbOJmoIDu7\n23CdP8JDNgAAADvpN37jN7a7fuWVV+bJT35yfvmXf3lEFY0n55EFAAAYU1/+8pdz7LHHpkbZr3oM\nTXSQXb7n8tT5td3FLMUAAEAX3H333bnjjjty3HHHbXf7xRdfPKKKxsdEdS2ezfhYAACgK+67776c\ncsopeelLX5r3vve9ueyyy5IkK1eu3PaY22+/Pd/+9rdHVeLYmOgWWQAAgK646qqrcsMNN2TZsmX5\nyU9+ks997nPZf//988ADDySZOr/su9/97px33nkjrnT0qo3h1F9V1fqpq84v54gFAIAxVVUZx/wx\nLn7yk5/krW99a5YtW5ZNmzblPe95T+66665ccMEFeeYzn5ktW7ZkzZo1Ofjgg0dd6px25vWdfmzf\nA38FWQAAYCgE2ck2zCCrazEAAACdIsgCAADQKYIsAAAAnSLIAgAA0CmCLAAAAJ2y26gL6NeKC1dk\n40Mbt7tt+Z7LR1QNAAAAw9LZILvxoY1OtQMAALAE6VoMAABApwiyAAAAdIogCwAAQKcIsgAAAHSK\nIAsAAECnjCTIVtXbquqvq+rWqvrzqtpjFHUAAADQPUMPslV1YJKzkrywtfbcJE9M8mvDrgMAAIBu\nGtV5ZHdLsndVPZZk7yT3jKgOAAAAOmboLbKttXuS/H6S7yb5XpL7W2tXDLsOAAAAumnoLbJVtTzJ\nK5IcnORHSf7/qvo3rbVPzHzcmjVrtv1/9erVWb169fCKBAAAYNGsW7cu69atW7TlVWtt0RbW0wqr\n/nWSk1prr5++/ptJfqW19m9nPKYtVFedX2nvGW7tAABA/6oqw84fXfXII4/k2GOPzQMPPJBrr702\nK1asGHVJC9qZ13f6sdXvukYxa/HfJ/mVqtqrqirJiUluG0EdAAAAY+nRRx/NPffck3vvvTebNm0a\ndTljZ+hdi1trX6+qS5N8I8mj0/9+dNh1AAAAjKu99947d9xxRzZv3px999131OWMnaF3Le6FrsUA\nADB5dC2ebMPsWjyq0+8AAAAwy8aNG/P2t789Dz/8cDZv3pxLLrkkT3ziE7fdf+aZZ2bjxo35xCc+\nsYOlTL5RjJEFAABgDr/zO7+TCy64IB/96Edz6aWX5rLLLtt23+bNm3PxxRfn4YcfHmGF40GLLAAA\n0Al1ft89UXfZMIY13n777dl///1z0EEHZe3atUmS/ffff9v9N9xwQx588MGccMIJA69l3AmyAABA\nJ0z6HDn33XdfXvva1yZJLrroohxyyCE56qijtt1/9dVXJ0mOP/74kdQ3TnQtBgAAGAMvetGL8qxn\nPSvr16/P5z//+W2hdquvfOUrOeCAA/ILv/ALI6pwfAiyAAAAY+TSSy/NY489lle96lXbbtuyZUu+\n+tWvZvXq1aMrbIwIsgAAAGPk+uuvzzOe8Ywcdthh22679dZb86Mf/Ui34mmCLAAAwBj5/ve/n2c/\n+9nb3XbFFVckMT52q85M9rTiwhXZ+NDGbdeX77l8hNUAAAAMxqpVq/Kxj30sW7ZsyROe8ITcdNNN\nueCCC3LggQdu10q7lHUmyG58aOPEz1IGAABw3nnn5bvf/W5OOeWUHHroodlnn33y2GOP5SUvecmo\nSxsbnQmyAAAAS8XHP/7xbf+/9NJLs2nTprz61a8eYUXjxRhZAACAMXHSSSflaU97Wn784x8nmZqt\n+AMf+EBe+cpX5oQTThhxdeNDkAUAABgTN9xwQ4455pht3Ynf8pa3ZI899sif/dmfjbq0sVKtjd+4\n06pqs+uq88sYWQAA6LCqyjjmj3FyxRVX5Itf/GIefPDBrF+/Psccc0ze8pa35AlPGP82yJ15facf\nW32vaxzfSIIsAABMHkF2sg0zyI5/rAcAAIAZBFkAAAA6RZAFAACgUwRZAAAAOkWQBQAAoFMEWQAA\nADpFkAUAAKBTBFkAAAA6RZAFAACgUwRZAAAAOkWQBQAAoFMEWQAAADpFkAUAAKBTBFkAAAA6RZAF\nAAAYM4888kiOOuqoHHHEEdmwYcOoyxk7giwAAMCYefTRR3PPPffk3nvvzaZNm0ZdztjZbdQFAAAA\nsL299947d9xxRzZv3px999131OWMHUEWAABgDO21117Za6+9Rl3GWBJkAQAAxsgPf/jDnH/++Wmt\n5Tvf+U7OOOOMnHjiiTn33HOzxx575P7778+FF16Ypz/96aMudWQEWQAAgDHx8MMP53Wve10+/OEP\n56CDDsott9ySVatW5bTTTstHPvKRfOYzn8kZZ5yR5z//+TnnnHNGXe7ImOwJAABgTHzkIx/J2Wef\nnYMOOijJVPfizZs35wUveEH222+/VFWe97zn5bTTThtxpaOlRRYAAOiEj370oyNb9xve8IahrGfF\nihU5/vjjt13/xje+kSQ5+eSTkySnn356Tj/99KHUMs6qtTbqGh6nqtrsuur8SnvP+NUKAAD0pqoy\njvljnL3pTW/KJz/5yWzYsCFVNepydmhnXt/px/a9QboWAwAAjKkvf/nLOfbYY4ceYq+66qq8+MUv\nziGHHDLU9fZqbINsnV/bXZbvuXzUJQEAAAzN3XffnTvuuCPHHXfcdrdffPHFA1/3cccdl1e84hVZ\ntWrVwNfVj7EdI6sbMQAAsJTcd999OeWUU/LSl740733ve3PZZZclSVauXLntMbfffnu+/e1vD6We\nq6++Oi972cuGsq6dNbYtsgAAAEvJVVddlRtuuCHLli3LT37yk3zuc5/L/vvvnwceeCDJ1Pll3/3u\nd+e8884beC1btmzJNddcs93EU+OkM5M9AQAA3Waypx37yU9+kre+9a1ZtmxZNm3alPe85z256667\ncsEFF+SZz3xmtmzZkjVr1uTggw/e9jfvf//7c/PNN+e8887Ltddemx/84AfZZ599ctZZZyVJrrji\nilxzzTU58MADc/PNN+ecc87ZNu71S1/6UtauXZtDDz00rbWsXbs2l19+eZLkpptuystf/vLce++9\nPdc/zMmeBFkAAGAoBNnFde2112bZsmX55Cc/mW9+85v59Kc/nde//vV58MEH86lPfSqXXHJJvvjF\nL24bU/uBD3wgxx57bI4++uhceeWVOeuss/L1r389e++9d84888z87d/+bT7/+c8nSf7gD/4g119/\nfS655JKe6zFrMQAAADv0ve99Ly984Qtz3XXX5fTTT8/uu++ed73rXfnjP/7jbNq0KW9+85tz+OGH\n56KLLsoHP/jBrF69OkcffXRaa3njG9+Yt73tbdl7772TJPfff39Wr169bdlXXXXV2HYrTrTIAgAA\nQ6JFdvE9+OCDWbFiRe6+++7st99+226/7LLL8prXvCbr169/3N9cf/31Ofroo3PvvffmgAMOSJIc\nfPDB+dSnPpWjjjoqrbU87WlPy7XXXpvDDjus51q0yAIAALCga6+9Noceeuh2ITZJHnjggey///6P\ne/xjjz2WO++8MwceeOC2EHvnnXdmw4YNWblyZb72ta/l1ltvzbJly3LYYYdl3bp1w9iMnTaSIFtV\nT6mqS6vqm1V1W1X9yijqAAAA6LJ169Zt1yV4qxe96EW57777snnz5m23rV27NldccUWOPPLIPOEJ\nP42CH/rQh7Jy5cps3rw5N954Y771rW/lmGOOyQMPPJDbbrttGJux00bStbiqPp7kqtbax6pqtyRP\naq39aMb9uhYDAMCE0bV48f3qr/5qTj/99Jx00kmPu+8Tn/hErr/++hx55JF56KGHsmrVqhxzzDFJ\nkvPPPz977rlndt9996xatSoXXnhhVq5cmTPPPDOPPfZY3vSmN+WXfumXcu655+ZJT3pST7VM9KzF\nVfXkJDe11g7ZwWMEWQAAmDCC7GSb9DGyP5fkvqq6uKq+UVV/UlV7j6AOAAAAOmi3Ea3zl5Oc2Vr7\n71X1B0nemeR3Zz5ozZo12/6/evXqOft9AwAAMP7WrVu3qBNHjaJr8c8m+Vpr7eemrx+b5J2ttVNn\nPEbXYgAAmDC6Fk+2ie5a3Fr7hyR3VdVzpm86McnfDLsOAAAAumlUsxY/L8lFSZYl+R9JXmvWYgAA\nmGxaZCfbRM9a3AtBFgAAJo8gO9kmumsxAAAA7ApBFgAAgE4RZAEAAOgUQRYAAIBOEWQBAADoFEEW\nAACAThFkAQAA6BRBFgAAgE4RZAEAAOgUQRYAAGDMPPLIIznqqKNyxBFHZMOGDaMuZ+wIsgAAAGPm\n0UcfzT333JN77703mzZtGnU5Y6daa6Ou4XGqqo1jXQAAQP+qKvbze/fggw9m8+bN2XfffUddSk92\n5vWdfmz1va5xfCMJsgAAMHkE2ck2zCC7W79/CAAAwOLauHFj3v72t+fhhx/O5s2bc8kll+SJT3zi\ntvvPPPPMbNy4MZ/4xCdGWOXoaZEFAACGQovsws4888y8853vzPLly/MzP/MzWbt2bU455ZQkyebN\nm/OUpzwlL3vZy3LppZeOuNLHG2aLrMmeAAAAxsDtt9+e/fffPwcddFC+/OUvJ0n233//bfffcMMN\nefDBB3PCCSeMqsSxoWsxAADQCR/96EdHtu43vOENA1/Hfffdl9e+9rVJkosuuiiHHHJIjjrqqG33\nX3311UmS448/fuC1jDtdiwEAgKHQtbg369evz0EHHZQ1a9bkt3/7t7fdfuqpp+bGG2/MvffeO8Lq\n5qdrMQAAwBJ16aWX5rHHHsurXvWqbbdt2bIlX/3qV7N69eqBr/+qq67Ki1/84hxyyCEDX1e/BFkA\nAIAxcv311+cZz3hGDjvssG233XrrrfnRj340lG7Fxx13XF7xildk1apVA19XvwRZAACAMfL9738/\nz372s7e77YorrkgyvPGxV1999VBaf/slyAIAAIyRVatW5c4778yWLVuSJDfddFMuuOCCHHjggdu1\n0g7Kli1bcs0114z1pFJmLQYAABgj5513Xr773e/mlFNOyaGHHpp99tknjz32WF7ykpdse8z73//+\n3HzzzTnvvPNy7bXX5gc/+EH22WefnHXWWUmmWnCvueaaHHjggbn55ptzzjnnbBvz+qUvfSlr167N\noYcemtZa1q5dm8svv3zbsm+++ebsscceOeKII4a74TtBkAUAABgzH//4x7f9/9JLL82mTZvy6le/\nOkly7bXX5oQTTsh9992Xd7zjHfn0pz+d17/+9XnwwQdz1lln5ZJLLskXv/jFXHzxxUmSD3zgA1m/\nfn0OOeSQXHnllTn77LPz9a9/PXvvvXfOPPPM7L777tut+6qrrhrrbsWJrsUAAABj46STTsrTnva0\n/PjHP04y1c33Ax/4QF75ylfmhBNOSJJ873vfywtf+MJcd911Of3007P77rvnXe96V/74j/84mzZt\nypvf/OYcfvjhueiii/LBD34wq1evztFHH53WWt74xjfmbW97W/bee+8kyf333/+40HrVVVeNdbfi\nxHlkAQCAIXEe2YXtt99+WblyZS677LJs2bIlZ599dm655ZZ84QtfyJOe9KRtj3vwwQezYsWK3H33\n3dlvv/223X7ZZZflNa95TdavX/+4ZV9//fU5+uijc++99+aAAw5Ikhx88MH51Kc+laOOOipJ0lrL\n0572tFx77bU7PR7XeWQBAACWoE9+8pN53vOel7e85S359V//9fz8z/981q1bt12ITaa6Fx966KHb\nhdgkeeCBB7L//vs/brmPPfZY7rzzzhx44IHbQuydd96ZDRs2ZOXKlfna176WZOo0P8uWLcthhx2W\ndevWDWYjF4ExsgAAAGPixBNPzIknnrjg49atWzfnONYXvehFue+++7J58+ZtY1/Xrl2bZcuW5cgj\nj8wTnvDTtswPfehDWblyZTZv3pwbb7wxRx99dL75zW/mmGOOyQMPPJDbbrttbMfK6loMAAAMha7F\ni+dXf/VXc/rpp+ekk0563H2f+MQncv311+fII4/MQw89lFWrVuWYY45Jkpx//vnZc889s/vuu2fV\nqlW58MILs3Llypx55pl56lOfmvXr1+dNb3pTfumXfinnnnvu41qCd2SYXYsFWQAAYCgE2clmjCwA\nAADMQ5AFAACgUwRZAAAAOkWQBQAAoFMEWQAAADpFkAUAAKBTBFkAAAA6RZAFAACgUwRZAAAAOkWQ\nBQAAoFN2G3UBAADA0lFVoy6BCSDIAgAAQ9FaG3UJTAhdiwEAAOgUQRYAAIBOEWQBAADoFEEWAACA\nThlZkK2qJ1bVTVW1dlQ1AAAA0D2jbJE9O8ltSUxdBmNk3bp1oy4BliSfPRgNnz3oppEE2ao6KMnL\nk1yUxImkYIz4QYfR8NmD0fDZg24aVYvsh5L8+yRbRrR+AAAAOmroQbaqTk3y/dbaTdEaCwAAwE6q\n1oY7RLWq/o8kv5nk0SR7Jtk3yV+01l494zHGzQIAAEyw1lrfDZtDD7LbrbzquCT/rrV22siKAAAA\noFPG4TyyWl8BAADo2UhbZAEAAGBnjUOL7Haq6uSq+lZVfaeq3jHqemCSVdWdVXVLVd1UVV+fvm1F\nVV1eVbdX1Rer6imjrhO6rqo+VlXrq+rWGbfN+1mrqndN/w5+q6peOpqqofvm+eytqaq7p3/7bqqq\nl824z2cPFkFVPbOqrqyqv6n6n+3df6jddR3H8ecL50SnUSHMtNUkJrSgPIzUGNZMGEo0+4EtI5gQ\nFfRjVvTHYlRQEEVUo6wgWjEkthai7B/TNUSiwWK2NmUSSl4wW7MwSc3grt79cT6Xjodz7c773c49\nh+cDDuf7/Xw/3+/53Avv+77v8/mc78nDSba29s5y35IqZJOcA9wO3ACsBW5J8sbxjkqaagVsqKpe\nVV3V2rYB+6vqCuBA25e0OD+ln9sGjYy1JGuBzfTz4A3AD5IsqXwtTZBRsVfAt1vu61XVPWDsSR2b\nBT5bVW8CrgE+2eq6znLfUgvOq4DHqmqmqmaBPcBNYx6TNO2G7xa3CdjVtncB7zm7w5GmT1X9Gvj7\nUPN8sXYTsLuqZqtqBniMfn6UdJrmiT0Y/RWQxp7Ukar6S1X9vm0/BzwCXEaHuW+pFbKXAU8M7P+p\ntUk6Mwr4VZLDST7a2lZW1cm2fRJYOZ6hSVNvvli7lH7+m2MulLr36SRHk+wcWNpo7ElnQJLVQA84\nRIe5b6kVst55Sjq71ldVD7iR/pKPawcPVv9ucMaldIYtINaMQ6k7PwQuB64ETgDfeom+xp60CEku\nBO4EbquqZwePLTb3LbVC9klg1cD+Kl5cmUvqUFWdaM9/Be6iv4TjZJJLAJK8BnhqfCOUptp8sTac\nC1/b2iR1oKqeqgb4Mf9bvmjsSR1Kci79IvaOqrq7NXeW+5ZaIXsYWJNkdZLl9D/wu2/MY5KmUpIL\nklzUtlcAG4GH6MfcltZtC3D36CtIWqT5Ym0f8MEky5NcDqwBfjuG8UlTqf3zPOe99HMfGHtSZ5IE\n2Akcr6odA4c6y33Luh3y4lTVqSSfAu4FzgF2VtUjYx6WNK1WAnf1/86wDPhZVd2X5DCwN8lHgBng\nA+MbojQdkuwG3gFcnOQJ4EvA1xkRa1V1PMle4DhwCvhE+aXv0ssyIva+DGxIciX9ZYuPAx8HY0/q\n2Hrgw8CxJEda2xfoMPfF+JQkSZIkTZKltrRYkiRJkqSXZCErSZIkSZooFrKSJEmSpIliIStJkiRJ\nmigWspIkSZKkiWIhK0mSJEmaKBaykiQtQJJ/JznSHr9L8vokv2nHVid5qG2/JcmNHbze9iQPJzna\nXvOtrf0zSc5f7PUlSZpky8Y9AEmSJsQ/q6o31LZ+RL8esA64Z6EXTrKsqk4N7L8NeBfQq6rZJK8G\nzmuHbwPuAF44ncFLkjRNnJGVJOllSvLc0P65wFeAzW0W9eYkK5L8JMmhNpO7qfW9Ncm+JAeA/UOX\nvgT4W1XNAlTV01V1IslW4FLg/nYeSTYmOZjkwSR7k6xo7TNJvpHkWHvtN5zRX4YkSWeRhawkSQtz\n/sDS4jtbWw12aIXnF4E9VdWrql8A24EDVXU18E7gm0kuaKf0gPdX1XVDr3UfsCrJH5J8P8nb2/W/\nC/wZ2FBV1ye5uF3/+qpaBzwIfG5gbM9U1ZuB24Ednf0mJEkaM5cWS5K0MC+MWFo8Stpjzkbg3Uk+\n3/bPA15Hv9DcX1XPDF+gqp5Psg64FrgO+HmSbVW1a6jrNcBa4GASgOXAwYHju9vzHuA7Cxi7JEkT\nwUJWkqQz731V9ehgQ5KrgefnO6Gq/gM8ADzQbiS1BRguZKFfDH9oAWOo/99FkqTJ4NJiSZK69Q/g\nooH9e4GtcztJ5mZ1B2dtXyTJFUnWDDT1gJm2/SzwirZ9CFg/9/nX9nncwfM2DzwPztRKkjTRnJGV\nJGlhRs1o1ojt+4FtSY4AXwO+CuxIcoz+G8h/BDa1/vPNkl4IfC/JK4FTwKPAx9qxHwG/TPJk+5zs\nrcDuJHN3Nd7e+gO8KslR4F/ALafzw0qStJSlypVGkiRNmySPA+uq6ulxj0WSpK65tFiSpOnkO9WS\npGeHkxEAAABDSURBVKnljKwkSZIkaaI4IytJkiRJmigWspIkSZKkiWIhK0mSJEmaKBaykiRJkqSJ\nYiErSZIkSZooFrKSJEmSpInyXwqyhfwjOoxCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10968c450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.step(range(len(measurements[0])),dxt, label='$\\dot x$')\n",
    "plt.step(range(len(measurements[0])),dyt, label='$\\dot y$')\n",
    "\n",
    "plt.axhline(vx, color='#999999', label='$\\dot x_{real}$')\n",
    "plt.axhline(vy, color='#999999', label='$\\dot y_{real}$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.title('Estimate (Elements from State Vector $x$)')\n",
    "plt.legend(loc='best',prop={'size':22})\n",
    "plt.ylabel('Velocity')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement Uncertainty R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109f94c50>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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058b2YKn9vNYtSQqtLplpTXZorWuuk2+jT2dMPKPH543sN1L98vrp7fK3k1RZ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\nswhaAQAAAACe9X88k0xD53RAkAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10968c1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.semilogy(range(len(measurements[0])),Rdx, label='$\\dot x$')\n",
    "plt.semilogy(range(len(measurements[0])),Rdy, label='$\\dot y$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Measurement Uncertainty $R$ (Adaptive)')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUAAAAAWCAYAAACxMEX0AAAABHNCSVQICAgIfAhkiAAABUNJREFU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\n",
      "text/latex": [
       "$$\\left ( -100.0, \\quad 500.0, \\quad -50.0, \\quad 250.0\\right )$$"
      ],
      "text/plain": [
       "(-100.0, 500.0, -50.0, 250.0)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Tkqzr5/WH0l09ntL/Z619xdp879rvbXdNBxxwQC644IIsX748d911Vx599NF85CMfSSkv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\nyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b053d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,16))\n",
    "plt.scatter(xt,yt, s=20, label='State', c='k')\n",
    "plt.scatter(xt[0],yt[0], s=100, label='Start', c='g')\n",
    "plt.scatter(xt[-1],yt[-1], s=100, label='Goal', c='r')\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, between Filter Step 100 and 150 you have massive noise in the measurement, but the adaptive filter is raising the measurement covariance (R), so that the Kalman Gain is tryin to use the dynamic of the model instead of the measurement."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
